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Atlas › Integer Profiles › Node 37,123,785

37,123,785

33 × 5 × 73 × 3767
Deficient Odd Composite

37,123,785 factors as 3^3 × 5 × 73 × 3767. Its 32 positive divisors give a proper-divisor sum of 29,795,895, so this integer is deficient. The Collatz stopping time is 183 steps.

Prime Factor Structure

Factorization String 3^3 × 5 × 73 × 3767
Distinct Prime Factors 4
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 66,919,680
Proper Divisor Sum 29,795,895
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #37123783 ← → #37123787

Radix Representation

Decimal 37123785
Binary 10001101100111011011001001 (26 bits)
Octal 0o215473311
Hexadecimal 0x23676C9

Divisor Catalog (32)

1 3 5 9 15 27 45 73 135 219 365 657 1,095 1,971 3,285 3,767 9,855 11,301 18,835 33,903 56,505 101,709 169,515 274,991 508,545 824,973 1,374,955 2,474,919 4,124,865 7,424,757 12,374,595 37,123,785

Collatz Trajectory (183 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

37,123,785 111,371,356 55,685,678 27,842,839 83,528,518 41,764,259 125,292,778 62,646,389 187,939,168 93,969,584 46,984,792 23,492,396 11,746,198 5,873,099 17,619,298 8,809,649 26,428,948 13,214,474 6,607,237 19,821,712 9,910,856 4,955,428 2,477,714 1,238,857 3,716,572 1,858,286 929,143 2,787,430 1,393,715 4,181,146 2,090,573 6,271,720 3,135,860 1,567,930 783,965 2,351,896 1,175,948 587,974 293,987 881,962 440,981 1,322,944 661,472 330,736 165,368 82,684 41,342 20,671 62,014 31,007 93,022 46,511 139,534 69,767 209,302 104,651 313,954 156,977 470,932 235,466

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